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An Isaac Newton Institute Workshop

Model Theory, Algebraic and Analytic Geometry

HOMOTOPY TYPES OF FIBRES OF PFAFFIAN MAPS

Author: N Vorobjov (Bath)

Abstract

We prove a tight upper bound on the number of different homotopy types of fibres of semialgebraic, quadratic or semi-Pfaffian maps in terms of formats of these maps. A similar argument leads to a tight upper bound on the sizes of finite bisimulations of Pfaffian dynamical and hybrid systems.